The present invention relates generally to methods and apparatus for performing fracturing operations, and more specifically relates to methods and apparatus for modeling a fracture to determine a non-uniform conductivity in the fracture and for performing the fracturing operation by supplying proppant during the operation according to a schedule determined in response to a non-uniform conductivity in the fracture.
Various techniques or systems are used in the oil industry for increasing the production of oil or gas wells. One method known for stimulating a well is known as "hydraulic fracturing." During a typical hydraulic fracturing operation, a slurry including a viscous base fluid and a solid particulate material, particularly referred to as a "proppant," is pumped down the well at sufficient pressure to fracture open the producing formation surrounding the well. Once a fracture has been created, the pumping of the slurry is typically continued until a sufficient volume of the proppant has been carried by the slurry into the fracture. After a suitable time, the pumping operation is stopped, at which time the proppant residue will prop open the fracture in the formation, preventing it from closing. As a result of the fracture, the effective flow area from the producing formation is enlarged, thereby increasing the wells' production.
Typically, the slurry will be introduced into the well in stages, with each stage increasing in slurry volume and/or proppant concentration in the slurry. The repesentation of these volume stages and the accompanying proppant concentrations, is known as the proppant schedule.
The effectiveness of the fracturing operation is a function, in part, of the degree to which the propped fracture will allow fluid from the formation to flow from the formation, through the fracture to the well bore. This property is known as the conductivity of the fracture. The fracture conductivity is determined primarily by the size of the proppant particles and the volume of proppant within the fracture. The amount of proppant placed in the fracture must be sufficient to hold the fracture open. However, if too great a volume of proppant is placed in the fracture, the proppant will, in extreme cases, provide a relative barrier to fluid flow. A common disadvantage of utilizing a greater amount of sand than is actually needed is the increased possiblity of "sand out" (a blockage of the fracture due to excess sand), causing premature termination of the fracturing operation. Another common disadvantage resulting from placing too much proppant in the fracture is the potentially dramatic increase in the cost of the fracturing operation due to the cost of the excess proppant.
Prior art techniques of determining the proppant concentration for a particular fracture have been based upon achieving a uniform conductivity through the propped fracture. The ability of the propped fracture to conduct fluid is thus intended to be the same proximate the tip of the fracture as it is at the wellbore. Accordingly, proppant schedules developed in accordance with prior art techniques call for introducing proppant into the fracturing fluid in sufficient quantities to achieve a uniform conductivity. However, the flow rate through a fracture decreases with distance away from the wellbore. Thus, for any given fracture conductivity at the wellbore which is sufficient to produce hydrocarbons from a particular formation, a lesser conductivity will be sufficient to produce from the formation at locations of the fracture removed from the wellbore, since the flow rate through such locations is lower. The conductivity at such removed locations need only be sufficient to maintain a low pressure gradient towards the wellbore.
Accordingly, Applicant's invention provides a new method of modeling a fracture to determine a desired non-uniform conductivity over the length of the fracture and for determining a proppant concentration for a propped well in response to a desired non-uniform conductivity in the formation. This proppant concentration will yield flow characteristics from the fracture comparable to those achieved with a uniform proppant concentration. Thus, a proppant concentration determined in accordance with the present invention will facilitate fracturing a formation and propping the fracture with a reduced volume (and therefore cost), of proppant, relative to that required with prior art techniques, while achieving comparable flow characteristics from the fracture.